The Hubbard Model

In the slightly more than thirty years since its formulation, the Hubbard model has become a central component of modern many-body physics. It provides a paradigm for strongly correlated, interacting electronic systems and offers insights not only into the general underlying mathematical structure of many-body systems but also into the experimental behavior of many novel electronic materials. In condensed matter physics, the Hubbard model represents the simplest theoret ical framework for describing interacting electrons in a crystal lattice. Containing only two explicit parameters - the ratio ("Ujt") between the Coulomb repulsion and the kinetic energy of the electrons, and the filling (p) of the available electronic band - and one implicit parameter - the structure of the underlying lattice - it appears nonetheless capable of capturing behavior ranging from metallic to insulating and from magnetism to superconductivity. Introduced originally as a model of magnetism of transition met als, the Hubbard model has seen a spectacular recent renaissance in connection with possible applications to high-Tc superconductivity, for which particular emphasis has been placed on the phase diagram of the two-dimensional variant of the model. In mathematical physics, the Hubbard model has also had an essential role. The solution by Lieb and Wu of the one-dimensional Hubbard model by Bethe Ansatz provided the stimulus for a broad and continuing effort to study "solvable" many-body models. In higher dimensions, there have been important but isolated exact results (e. g. , N agoaka's Theorem).

Inhalt
Solvable Models, Rigorous Results, and Advances in Formalism.- The Hubbard Model: Some Rigorous Results and Open Problems.- On the Bethe Ansatz Soluble Degenerate Hubbard Model.- Thermodynamical Properties of the Exactly Solvable 1/r-Hubbard and 1/r-tJ Model.- Hierarchy of 1-D Electron Models with Long-Range Interaction.- One-Dimensional Luttinger Liquid of Particles for a Class of Infinitely Repulsive Interactions: Exact Solutions.- Exact Results for Spin and Charge Dynamics of Electrons with Supersymmetry.- Hidden Symmetry of Strongly Correlated Fermions.- Symmetries of Strongly Correlated Electrons.- Exact Results on a Supersymmetric Extended Hubbard Model.- Functional Integrals for Correlated Electrons.- Charge-Spin Separation and Pairing in a Generalized Hubbard Model.- A Renormalization Procedure for the Hubbard Model.- New Operator Algebra for the Hubbard Chain.- Exact Results and Conjectures on the Adiabatic Holstein-Hubbard Model at Large Electron-Phonon Coupling.- Ferromagnetism in Correlated Electron Systems: A New Class of Rigorous Criteria.- Infinite in All Directions: Large Coupling, High Dimensions, and Many Components.- The Mott Transition in Infinite Dimensions: Old Ideas and Some Surprises.- The Hubbard Model with Local Disorder in d = Infinity.- The Hubbard Model with Infinite Interaction: Magnetic Properties.- The Extended Hubbard Model at Large Interaction.- Drude Weight and f-Sum Rule of the Hubbard Model at Strong Coupling.- The Gutzwiller Projector in the Large U-Hubbard Model.- Revising the 1/N Expansion for the Slave-Boson Approach within the Functional Integral.- Fermi Liquid versus Luttinger Liquid.- Infarared Catastrophe: When Does It Trash Fermi Liquid Theory?.- Two-Particle Scattering and Orthogonality Catastrophe in the HubbardModel.- Failure of Fermi Liquid Theory in 2-Dimensions: How to Infer it from Peturbation Theory.- Conservation Laws in Normal Metals: Luttinger Liquid vs. Fermi Liquid.- Charge-Spin Separation and the Spectral Properties of Luttinger Liquids.- Non-Fermi Behavior in the Kondo and Heisenberg Models.- Luttinger-Liquid Behavior in 2-D: The Variational Approach.- Non-Fermi Liquid Behavior of Electrons in the 2-D Honeycomb Lattice: A Renormalization Group Analysis.- Search for Deviations from Fermi Liquid Behavior in 2-D Repulsive and Attractive Hubbard Models.- Perturbative, Mean Field, Variational, and Numerical Studies.- Hartree-Fock and RPA Studies of the Hubbard Model.- From One- to Two-Dimensions in the Weak Coupling Limit.- Metal-Insulator Transition in the 2-D Hubbard Model: A Fermionic Linearization Approach.- The Phase Diagram of the One-Dimensional Extended Hubbard Model.- Quantum-Monte-Carlo Simulations of Correlation Functions for the One-Dimensional Hubbard Model.- Quantum-Monte-Carlo Studies of One- and Two-Dimensional Hubbard Models.- Effect of Disorder on Several Properties of the One-Band Hubbard Model in 2-D.- The Wavefunction Renormalization Constant for the One- and Two-Band Hubbard Hamiltonians in Two-Dimensions.- Experiments and Physical Applications.- Electron Spectroscopy and Hubbard: Issues and Opportunities.- On Electrical Properties of Chalcogenide Glassy Semiconductors in the Framework of Hubbard Model with Negative Correlation Energy.- The Metal Insulator Transition in the Hubbard Model.- Metal to Insulator Transition in the 2-D Hubbard Model: A Slave-Boson Approach.- The Hubbard Model and Its Application to Conjugated ?-Electron Systems.